Q: May a layperson assist with the sprinkling rite at Mass; that is, also sprinkle a part of the assembly as the priest sprinkles another part? It would seem not, given that in Pastoral Care of the Sick, a layperson is not mentioned as being able to sprinkle with holy water (e.g., #82 – deacon and priest are specifically mentioned, and the praenotanda notes that the text is very careful in mentioning which ministers can do what [#44]).
A: I share your interpretation of this. The missal makes no provision for a layperson assisting in the sprinkling of water at Mass.
You are correct also about Pastoral Care of the Sick. The sprinkling with blessed water is reserved to the priest or deacon. That helps with an interpretation, even though I exercise caution in applying the rubrics from one ritual into the rubrics of another. After all, the Book of Blessings permits a lay presider to sprinkle, such as when visiting a cemetery (1746).
At Mass, the priest sprinkles. There is not even a provision for the deacon to assist him. I interpret this to mean that this action is a function of the priest’s role as the celebrant of the Mass.
He sprinkles the people “moving through the church, if appropriate.” But if the distances are great, and if this would cause an excessive delay, he may just sprinkle from the sanctuary, an action resembling that of the minister who incenses the people during the preparation of the gifts.